Here I have a few sentences with seemingly obscure usages of という appearing after the こそ and は particles.
Firstly, while watching からかい上手の高木さん I came across this particular sentence in Ep. 3 @11:22:
この苦しみを噛み締めながら次こそはという意識を高めるのだ
Translation Attempt: While I digest this pain I'll increase my awareness for next time.
Context: 西片 is enforcing a punishment on himself because he is getting teased by 高木 all day, every day. In this scene where he says this line, he's doing push-ups (the aforementioned punishment).
After attempting to research this usage, the only things I could find were sentences from a youtube subtitle database that all seemed to start the same with「我こそは」such as:
我こそはという方はぜひお願いいたします
https://youtu.be/zLKYvB_HfWg @1:46
我こそはという半導体関係であったり電子部品の会社であったり
https://youtu.be/ewKRCv9g_RQ @43:04
Is this merely a rare usage of という? If so, what is the purpose? Is it adding emphasis? Or could it be that 「こそはという」is some sort of set expression that has a particular meaning? I'm aware that という will not translate easy, but any further elaboration on the translation of the first sentence I provided, in order to show the function that という is performing, would be wonderful. Also, do let me know if I need to provide any further details or context.